A domain-theoretic framework for robustness analysis of neural networks

摘要

A domain-theoretic framework is presented for validated robustness analysis of neural networks. First,global robustness of a general class of networks is analyzed. Then, using the fact that Edalat’s domaintheoreticL-derivative coincides with Clarke’s generalized gradient, the framework is extended for attackagnosticlocal robustness analysis. The proposed framework is ideal for designing algorithms which arecorrect by construction. This claim is exemplified by developing a validated algorithm for estimationof Lipschitz constant of feedforward regressors. The completeness of the algorithm is proved over differentiablenetworks and also over general position ReLU networks. Computability results are obtainedwithin the framework of effectively given domains. Using the proposed domain model, differentiable andnon-differentiable networks can be analyzed uniformly. The validated algorithm is implemented usingarbitrary-precision interval arithmetic, and the results of some experiments are presented. The softwareimplementation is truly validated, as it handles floating-point errors as well.